A theoretical analysis of haemoglobin (Hb) concentration detection is presented in this work with the objective of achieving more sensitive detection and monitoring low concentrations. Surface-enhanced SPR spectroscopy on silver nanoparticles was employed for recording Hb concentrations less than 10 g/L. In this paper, Fe₃O₄@Au core-shell, nanocomposite spherical nanoparticle consisting of a spherical Fe₃O₄ core covered by Au shell, was used as an active material for biomolecules detection in the Surface Plasmon Resonance (SPR)-based biosensor in the wavelength 632.8 nm. We present the simulation of detection amplification technique through Attenuated Total Reflection (ATR) spectrum in the Kretschmann configuration. The system consists of a four-layer material i.e prism/Ag/Fe₃O₄@Au+Hb/air. Dielectric function determination of the core-shell nanoparticle (Fe₃O₄@Au) and the composite (Fe₃O₄@Au+Hb) was done by applying the Effective Medium Theory approximation and the calculation of the reflectivity is carried out by varying the size of core-shell (r₀). In this simulation, the refractive index of the BK7 prism is 1.51; the refractive index of Ag thin film is 0.13455+3.98651i with the thickness of 40 nm, and the refractive index of the composite is varied depending on the size of nanoparticle core-shell. Our results show that by varying the radius of the core and the shell thickness, the dip of the reflectivity (ATR) spectrum is shifted to the larger angle of incident light and the addition of core-shell in the conventional SPR-based biosensor leads to enhancement of the SPR biosensor sensitivity, for the core-shell radius 10 nm, the sensitivity increased by 1.35% for F = 0.1, and by 4.89% for F =0.8 compared to the sensitivity of the conventional SPR-based biosensor without core-shell addition.